# Representations of algebraic groups in prime characteristics

Annales scientifiques de l'École Normale Supérieure (1981)

- Volume: 14, Issue: 1, page 61-76
- ISSN: 0012-9593

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topKempf, George R.. "Representations of algebraic groups in prime characteristics." Annales scientifiques de l'École Normale Supérieure 14.1 (1981): 61-76. <http://eudml.org/doc/82067>.

@article{Kempf1981,

author = {Kempf, George R.},

journal = {Annales scientifiques de l'École Normale Supérieure},

keywords = {connected reductive group; rational irreducible representations; Steinberg representations; Mumford's conjecture; cohomology of sheaves on homogeneous space; group schemes},

language = {eng},

number = {1},

pages = {61-76},

publisher = {Elsevier},

title = {Representations of algebraic groups in prime characteristics},

url = {http://eudml.org/doc/82067},

volume = {14},

year = {1981},

}

TY - JOUR

AU - Kempf, George R.

TI - Representations of algebraic groups in prime characteristics

JO - Annales scientifiques de l'École Normale Supérieure

PY - 1981

PB - Elsevier

VL - 14

IS - 1

SP - 61

EP - 76

LA - eng

KW - connected reductive group; rational irreducible representations; Steinberg representations; Mumford's conjecture; cohomology of sheaves on homogeneous space; group schemes

UR - http://eudml.org/doc/82067

ER -

## References

top- [1] H. H. ANDERSEN, On the Structure of the Cohomology of Line Bundles on G/B (to appear).
- [2] H. H. ANDERSEN, The Frobenius Morphism on the Cohomology of Homogeneous Vector Bundles on G/B (to appear). Zbl0421.20016
- [3] A. BOREL, Linear Algebraic Groups, Benjamin, New York, 1969. Zbl0186.33201MR40 #4273
- [4] A. BOREL et al., Seminar on Algebraic Groups and Related Finite Groups (Lecture Notes in Math., No 131, Springer-Verlag, Berlin, 1970). Zbl0192.36201MR41 #3484
- [5] E. CLINE, B. PARSHALL and L. SCOTT, Induced Modules and Extensions of Representations (Inventiones Math., Vol. 41, (1978, pp. 41-51). Zbl0399.20039MR58 #16897
- [6] C. W. CURTIS, Representation of Lie Algebras of Classical Type with Applications to Linear Groups (J. Math. and Mech., Vol. 9, 1960, pp. 307-326). Zbl0089.25302MR22 #1634
- [7] W. HABOUSH, Reductive Groups are Geometrically Reductive (Annals of Math., Vol. 102, 1975, pp. 67-84). Zbl0316.14016MR52 #3179
- [8] W. HABOUSH, A short Characteristic p Proof of the Kempf Vanishing Theorem (Inventiones Math.).
- [9] G. KEMPF, Linear Systems on Homogeneous Spaces (Ann. of Math., Vol. 103, 1976, pp. 557-591). Zbl0327.14016MR53 #13229
- [10] G. KEMPF, The Grothendieck-Cousin Complex of an Induced Representation (Advances in Math, Vol. 29, 1978, pp. 310-396). Zbl0393.20027MR80g:14042
- [11] R. STEINBERG, Prime Power Representations of Finite Linear Groups II (Can. J. Math., Vol. 9, 1957, pp. 347-351). Zbl0079.25601MR19,387d
- [12] R. STEINBERG, Representations of Algebraic Groups (Nagoya Math. J., Vol. 22, 1963, pp. 33-56). Zbl0271.20019MR27 #5870
- [13] M. SWEEDLER, Hopf Algebras, Benjamin, New York, 1969. Zbl0194.32901

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